Image copyright PA
Mr Assange, who has been questioned about a sex allegation in Sweden, spoke out a year after a UN legal panel ruled he should be allowed to walk free.
The UK Foreign Office previously said that finding "changes nothing".
In February 2016, the UN's Working Group on Arbitrary Detention found he was being "arbitrarily detained" by the UK and Sweden.
Mr Assange said a year on the two governments had failed to comply with the ruling.
"I call on UK and Sweden to do the right thing and restore my liberty," he said.
"These two states signed treaties to recognise the UN and its human rights mechanisms."
Who is Julian Assange?
Timeline: Julian Assange sex case
He said the UK and Swedish governments accepted the jurisdiction of the working group and did not withdraw from their 16-month investigation into his case.
Mr Assange went on: "They lost, appealed and lost again.
"This refusal to respect the umpire's decision comes at a terrible cost.
"Other states can now illegally detain Swedish and UK citizens with effective impunity and the UN human rights system more broadly is imperilled."
Mr Assange has been living in the embassy since 19 June 2012.
He sought asylum after a supreme court rejected his appeal against being extradited to Sweden to face sex assault allegations.
He reportedly lives in a small room with a bed, sun lamp, computer, shower, treadmill and cooking facilities.
Mr Assange has refused to travel to Sweden for questioning because he fears he will then be handed over to the US over Wikileaks' release of 500,000 secret military files.
WikiLeaks previously said its founder would agree to be extradited if clemency was granted to Chelsea Manning - who leaked documents to the website.
The transgender US Army private, born Bradley Manning, will be freed on 17 May after former US President Barack Obama commuted her sentence.
Mr Assange has said he would stand by his offer as long as his rights were protected.